Question: Simplify the following expression: $\dfrac{44a^4}{132a^3}$ You can assume $a \neq 0$.
Solution: $ \dfrac{44a^4}{132a^3} = \dfrac{44}{132} \cdot \dfrac{a^4}{a^3} $ To simplify $\frac{44}{132}$ , find the greatest common factor (GCD) of $44$ and $132$ $44 = 2 \cdot 2 \cdot 11$ $132 = 2 \cdot 2 \cdot 3 \cdot 11$ $ \mbox{GCD}(44, 132) = 2 \cdot 2 \cdot 11 = 44 $ $ \dfrac{44}{132} \cdot \dfrac{a^4}{a^3} = \dfrac{44 \cdot 1}{44 \cdot 3} \cdot \dfrac{a^4}{a^3} $ $\phantom{ \dfrac{44}{132} \cdot \dfrac{4}{3}} = \dfrac{1}{3} \cdot \dfrac{a^4}{a^3} $ $ \dfrac{a^4}{a^3} = \dfrac{a \cdot a \cdot a \cdot a}{a \cdot a \cdot a} = a $ $ \dfrac{1}{3} \cdot a = \dfrac{a}{3} $